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2 years ago

13

11 = - 5x - 2 help 11= -5x-2

2 answers:

mr Goodwill [35]2 years ago

7 0

Try to get X by itself so you have to add two to each side. Then get rid of the -5 by dividing it. The end result would be x= 13/-5

Natalija [7]2 years ago

3 0

$11 = -5x-2\\5x = -2-11\\5x =-13\\x = -13/5$

Answer: x = -13/5

Ok done. Thank to me :>

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Find the standard equation of a sphere that has diameter with the end points given below. (3,-2,4) (7,12,4)

DiKsa [7]

Answer:

The standard equation of the sphere is $(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

Step-by-step explanation:

From the question, the end point are (3,-2,4) and (7,12,4)

Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.

The midpoint can be calculated thus

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Let the first endpoint be represented as $(x_{1}, y_{1}, z_{1})$ and the second endpoint be $(x_{2}, y_{2}, z_{2})$ .

Hence,

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Midpoint = $(\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})$

Midpoint = $(\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\$

Midpoint = $(5, 5, 4)$

This is the center of the sphere.

Now, we will determine the distance (diameter) of the sphere

The distance is given by

$d = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} + (z_{2}- z_{1})^{2} }$

$d = \sqrt{(7 - 3)^{2} +(12 - -2)^{2} + (4- 4)^{2}$

$d = \sqrt{(4)^{2} +(14)^{2} + (0)^{2}$

$d = \sqrt{16 +196 + 0$

$d =\sqrt{212}$

$d = 2\sqrt{53}$

This is the diameter

To find the radius, r

From $Radius = \frac{Diameter}{2}$

$Radius = \frac{2\sqrt{53} }{2}$

∴ $Radius = \sqrt{53}$

r = $\sqrt{53}$

Now, we can write the standard equation of the sphere since we know the center and the radius

Center of the sphere is $(5, 5, 4)$

Radius of the sphere is $\sqrt{53}$

The equation of a sphere of radius r and center $(h,k,l)$ is given by

$(x-h)^{2} + (y-k)^{2} + (z-l)^{2} = r^{2}$

Hence, the equation of the sphere of radius $\sqrt{53}$ and center $(5, 5, 4)$ is

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}$

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

This is the standard equation of the sphere

6 0

3 years ago

7. A baseball has a radius of 2 inches. What is the volume in cubic inches of

Sever21 [200]

Answer:

33.49

Step-by-step explanation:

Volume of a sphere formula= 4/3πr^3

Radius= 2

Plug the radius into the formula to get your answer.

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4 years ago

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3 years ago

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3 years ago

90 x= 81 + 25 <br> I need help ?

charle [14.2K]

Answer:

$x = \frac {53} {45}$

Step-by-step explanation:

<u>Step 1: Combine on the right side </u>

$90x = 81 + 25$

$90x = 106$

<u>Step 2: Divide both sides by 90 </u>

$\frac {90x} {90} = \frac {106} {90}$

$x = \frac {106/2} {90/2}$

$x = \frac {53} {45}$

Answer: $x = \frac {53} {45}$

4 0

4 years ago

Read 2 more answers